Question: Simplify the following expression: $ x = -2 + \dfrac{-5}{-5a + 5} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5a + 5}{-5a + 5}$ $ \dfrac{-2}{1} \times \dfrac{-5a + 5}{-5a + 5} = \dfrac{10a - 10}{-5a + 5} $ Therefore $ x = \dfrac{10a - 10}{-5a + 5} + \dfrac{-5}{-5a + 5} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{10a - 10 - 5}{-5a + 5} $ $x = \dfrac{10a - 15}{-5a + 5}$ Simplify the expression by dividing the numerator and denominator by -5: $x = \dfrac{-2a + 3}{a - 1}$